There is an engine pumping liquid, for example, water, through a pipe. One way to figure out the engine's power is to times the force with the velocity of the liquid. The other way is to calculate the kinetic energy in the liquid per unit of time. Which is correct?
There is a similar question Work power energy contradiction in hose pipe problem [closed]. But it was closed due to the check-my-work and homework policy. Some answers on the Internet support the first way: times the force with the velocity.
- An engine pumps water through a hose pipe . Water passes through the pipe and leave with a velocity 2m/s. The mass per unit length of water in pipe is 100 kg/m . What is the power of the engine ?
- An engine pumps water through a pipe. Water passes through the pipe and leaves it with a velocity of 2 m / s. The mass per unit length of water in the pipe is 100 kg / m. What is the power of the engine?
However, some answers on physics.stackexchange.com support the second way: the engine power is equal to the kinetic energy.
- Power of water pump
- Power of a Hydraulic Pump and Rate at which Kinetic Energy is imparted to the water
Which is correct?
I didn't give any example in this post because I didn't want this post to get the same fate as Work power energy contradiction in hose pipe problem [closed] although I think this post has educational value. If you want to find examples, click the link. However, welcome to give examples. Examples are always the best way to demonstrate the concept and also a method we learn things from the fundamentals. This is true not only in the physics field.
Response from knzhou
knzhou is the author of the picked answer of Power of water pump. knzhou claimed the power of the engine should equal to the kinetic energy in the liquid per unit of time.
The physically correct answer is 400 W. As for what was marked "correct" on that test question, I have no idea -- it depends on whether the test writer knew what they were doing. Actually, many JEE prep problems are incorrectly posed, and don't have any correct answers.
Backup for the similar question
Work power energy contradiction in hose pipe problem [closed] has been deleted. I failed to cache the page with archive.org. To let others see the example, I copy-pasted that question from the page cached by Google.
- Author: Neel Narlawar
Question: An engine pumps water through a hose pipe. Water passes through the pipe and leaves it with a velocity of 2 m/s. The mass per unit length of water in the pipe is 100 kg/m. What is the power of the engine?
Approach 1:
Force = vdm/dt = 2(2×100) = 400
Power= Force × Velocity = 800W
800 is the answer given in most of the books out there.
Approach 2:
Change in kinetic energy of water = 1/2 * m * v^2
Rate = 1/2 * m/t * v^2 = 1/2 * 200 * 4 = 400W
I am unable to find an error in either of the approaches so can someone tell me what's wrong in the second approach? Both the concepts seem correct, the former being related to the usual force power relation while the second uses kinetic energy work relation. Is there a problem in my understanding of the concept? Thank you!
Note: I have tried looking at other sources for clarification but nothing seems to answer my question properly.
